What is 8log_{b}(x)+5log_{b}(z) ?

The solution to 8log_{b}(x)+5log_{b}(z) is log_{b}(x^8z^5)

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simplify 8log_{b}(x)+5log_{b}(z)

simplify

8 lo g_{b} (x) + 5 lo g_{b} (z)

lo g_{b} (x^{8} z^{5})

Solution steps

8 lo g_{b} (x) + 5 lo g_{b} (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

8 lo g_{b} (x) = lo g_{b} (x^{8})

= lo g_{b} (x^{8}) + 5 lo g_{b} (z)

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

5 lo g_{b} (z) = lo g_{b} (z^{5})

= lo g_{b} (x^{8}) + lo g_{b} (z^{5})

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

lo g_{b} (x^{8}) + lo g_{b} (z^{5}) = lo g_{b} (x^{8} z^{5})

= lo g_{b} (x^{8} z^{5})

lo g_{a} (m) - lo g_{a} (n) + lo g_{a} (p)

lo g_{5} (\frac{x ^{4}}{25 y ^{2} z})

lo g_{4} (64 x y)

ln (sin (θ)) - ln (\frac{sin ( θ )}{3})

ln (x) + \frac{1}{2} ln ((\frac{y}{x})^{2} + 2 (\frac{y}{x}) + 2)

What is 8log_{b}(x)+5log_{b}(z) ?
The solution to 8log_{b}(x)+5log_{b}(z) is log_{b}(x^8z^5)